Div-2 Safe Pressure thickness fails in combined load calculation 1

[BPVFEA]

Hi,
I am referring to ASME Sec VIII Div 2 Ed 2007 Add 2008
I calculate the safe pressre thickness of cylindrical shell by clause 4.3.1 t=D/2(exp(P/SE)-1)
Now I go to Cl 4.3.10.2 to calculate the stress under combined loading. I take only pressure load . (No moment, force, weight etc.)
I am surprised to find that the thickness t fails in combined stress calculation.
Some Designers feel that there is some mistake in the code & ASME will correct it. But I found that ASME has not corretced it in recent 2009 addenda.
I request your opinion on this,
1) Is ASME calculation given correct?
2) If not, then what is should be ?

Thanks in advance.

 

[TGS4]

In my experience, the calculations are correct. Please post your calculations here for review.

For example, if I use:
D=100in
P=2000psi
S=25000psi
E=1

Then, t=4.164in, and Do is 108.329in
sigma_theta-m=25000psi

Assuming no external net section force, no external bending moment, and no net section torsion moment (F=0, M=0, theta=0, and Mt=0), then
sigma_sm=11527psi
tau=0

sigma1=25000psi
sigma2=11521psi
sigma3=1000psi

sigma_eqv=20837psi, which is < 25000psi

 

[BPVFEA]

Sorry. It was my mistake. Actually my observation is regarding Spherical Shell (4.3.5.1 & 4.3.10.2.a.2) and not regarding cylindrical shell.
The Safe pressure thickness of spherical heads fails in combined stress calculation.
See the below example.

D = 200 in
P = 1000 psi
S = 25000 psi
E = 1.0
t = D/2*( exp( 0.5P/(S*E) )-1) = 2.0201 in (4.3.5.1)

Therefore, Do= 204.0402 in

When no external loads acting,

Sigma_theta_m = 25000 psi (4.3.35)
Sigma_s_m = 25000 psi (4.3.36)
Tau = 0 psi (4.3.37)

Sigma1= 25000 psi
Simga2= 25000 psi
Simga3= -500 psi

Equivalent Stress from Eq 4.3.44 would be
25500 psi > Allowable 25000 psi !!!!!!!!!!!!!!!!!!!!


TGS4- In your example sigma3 shall be negative i.e -1000psi
I feel that there would be some specific case in which cylindrial shell also may fail.

 

[BPVFEA]

Here is the example showing that it is applicable to Cylindrical Shell also, when shell is THICK

P=7000 psi
D=100 in
S=20000 psi
Required shell t by 4.3.1 is
t=20.95 in

Therefore Do= 141.90 in
Sigma_theta_m = 20000 psi
Sigma_s_m = 6905.03 psi
Sigma1 =20000 psi
Sigma2 = 6905.03 psi
Sigma2 = -3500 psi

Equivalent Stress from Eq 4.3.44 would be
20396 psi > Allowable 20000 psi !!!!!!!!!!!!!!!!!!!!

 

[TomBarsh]

This may or may not be related to the current question, but my ears perked up when I read that this was about spherical shells.

There is a typographical error in equation 4.4.55 (page 4-90), paragraph 4.4.7.1. The denominator has the ratio Fhe/Sy, this is transposed, the correct ratio is Sy/Fhe. This has been pointed out to the Code committee correction but did not make it in time for the 2009b Addenda.

The same typographical error exists in the original Code Case 2286 (and the corresponding nuclear code case). But the original derivation by Clarence Miller shows the correct ratio.

Using the ratio as currently published produces an unrealistic graphical plot of Pa versus nominal thickness when plotted for a given set of values for OD, Sy, and Ey. Hopefully nobody has used this for a nuclear job.

 

[TGS4]

Thanks for the heads-up Tom. It's not related, but very useful information.

BPVFEA - you are correct, the sigma3 should be negative. I agree with the results of your example posting (7 Oct 2:57).

Fundamentally, I don't think that there is any inconsistency with that specific result. The thickness equation is correct for thick or thin vessels. However, the combined loading equations are essentially stress linearization, which 5.2.1.3 says should not be used for R/t ratios less than or equal to 4. Your example above results in an R/t ratio of 2.386.

However, the fact that the selected thickness "fails" the combined loading analysis means that an increased thickness is required - a conservative measure in my opinion.

If you feel that there is something fundamentally wrong with this, please send a letter to the ASME Code Committee about it. However, I do not believe that there is any error, per se, in the existing text.

 

[BPVFEA]

Following is the explanation I had given to some other party when this issue came up. I request TGS4 & others for their views on this

========================================================
1) It seems, the pressure thickness formula for Div-2 t=D/2(exp(P/SE)-1) 4.3.1 is based on limit load.
Other way in the term of stress it would be S= P/ ln[(Di+2t)/Di] = P/ ln[Do/Di].
When I compared it with Lame's Equation, S is approximately matching with Hoop Stress at INNER Contour of Shell i.e ID S=P * (Do^2 + Di^2)/(Do^2 - Di^2)
I would like to mention here specifically that S is MAX stress in thickness and not the AVERAGE stress in thickness.

If we look into pressure thickness formula in old Div.2 was t = PR/(S-0.5P) AD-201(a) was based on stress intensity.
Other way in the term of stress it would be S= PR/t - (-0.5P). Here it is the difference of AVERAGE hoop stress & AVERAGE radial stress.

If we refer formula for AD-201(b) for thickness under External loading, the stress intensity is calculated based on AVERAGE stresses.
e.g sigma3=-0.5P is average radial stress.

2) Now coming to the Combined loading stress calculations as per 4.3.10.2 of new Div.2
Sigma_sm (4.3.33) & tau (4.3.34) are AVERAGE stresses, while Sigma_theta_m is the MAX stress in thickness.
I think the Problem we are facing in calculating Combined stress thickness is due to

a) Mixing up the average and max stresses in Combined Von Misses stress calculations. Here Average Sigma_theta_m needs to be used.
b) The theories used for Pressure Thickness & Combined load thickness being different (i.e limit load & Distortion energy respectively)

===================================================

TGS4- In short, the stress linearization of Sigma_theta_m componenet has not happened in combined loading equations.

 

[TGS4]

On first glance - your summary appears to make sense.

I would suggest that you write an inquiry to the Section VIII Code Committee with your concern and above-noted explanation. Perhaps then, at least you can receive an explanation from the Code Committee.